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Inequalities on Swan conductors

Abstract : In this thesis, we are concerned with smooth complex representations of the Weil group W of a non-Archimedean local field. Via the ramification filtration of W, one can attach to such a representation S an additive invariant sw(S), known as the Swan exponent. The central problem in this thesis is the following. For an n-dimensional representation S of W, we consider the composition ROS, where R denotes an algebraic representation of GL_n(C). We investigate the relations between sw(ROS) and sw(S). More precisely, we reprove certain results of Bushnell and Henniart in the case where R is the adjoint representation, only invoking Galois theory and elementary representation theory. Using similar methods, we also provide results when R is a tensor operation. Finally, we investigate the case n=2.
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Submitted on : Tuesday, May 19, 2020 - 5:22:08 PM
Last modification on : Wednesday, September 16, 2020 - 4:06:12 PM


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Ammar Yasir Kiliç. Inequalities on Swan conductors. Number Theory [math.NT]. Université Paris Saclay (COmUE), 2019. English. ⟨NNT : 2019SACLS309⟩. ⟨tel-02612976⟩



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